In the GAN setting both \(\hat{\Theta }_{n}(\tau _{n})\)  and \(\Theta _{0}\) 
are typically set-valued and not singletons and an appropriate notion
of distance between sets is required. One commonly used generalization
of the Euclidean distance \(|\cdot |\)  is the Hausdorff distance (see,
e.g., [1]}, or [2]}).
For any two non-empty bounded subsets \(A\)  and \(B\)  of some Euclidean
space, the Hausdorff distance between \(A\)  and \(B\)  is defined as
\(d_{H}(A,B)=\max \bigl \lbrace \sup _{a\in A}d(a,B),\sup _{b\in B}d(b,A)\bigr \rbrace ,\) 
